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Development of a photoresist is a complex physical process involving solid-to-liquid solution phase transition where a developer solution dissolves a section of a patterned resist. The developer can be selective towards either the exposed region (positive-tone) or the unexposed region (negative-tone). Accurate estimation of the development effects is crucial to the prediction of critical dimension (CD) in lithography simulations. Traditionally, the development effects have been captured by a front-propagation equation (such as Mack model and other similar models), which features a development front with a velocity dependent on the resist’s de-protection level. For a positive-tone development (PTD), due to the aqueous nature of the developer, where an exposed part of resist quickly dissolves when in contact with a developer, such a moving front simulates the development process accurately. However, in case of a negative-tone development (NTD), the rate of reaction and resist contrast is significantly lower than for PTD. Therefore it is important to take into account both the developer’s finite diffusion into resist and its reaction rate with the resist to reliably model the development process. In this paper, we discuss the mathematical model of resist’s development by taking into account the transport phenomena of diffusion and reaction taking place during the development step. The finite-element method is used to solve these reaction-diffusion equations over the non-trivial geometry of a patterned resist. We will analyze the results of reaction-diffusion process in comparison to the front propagation methods. The contribution of different model parameters will be described by studying the development rate for resist’s de-protection level and comparing it to the development rate obtained experimentally. We will briefly discuss the results from three dimensional lithographic patterns, which exhibit strong NTD effects.
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